Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

A Statistical Convergence Perspective of Algorithms for Rank Aggregation from Pairwise Data

Abstract: There has been much interest recently in the problem of rank aggregation from pairwise data. A natural question that arises is: under what sorts of statistical assumptions do various rank aggregation algorithms converge to an 'optimal' ranking? In this paper, we consider this question in a natural setting where pairwise comparisons are drawn randomly and independently from some underlying probability distribution. We first show that, under a 'time-reversibility' or Bradley-Terry-Luce (BTL) condition on the distribution, the rank centrality (PageRank) and least squares (HodgeRank) algorithms both converge to an optimal ranking. Next, we show that a matrix version of the Borda count algorithm, and more surprisingly, an algorithm which performs maximum likelihood estimation under a BTL assumption, both converge to an optimal ranking under a 'low-noise' condition that is strictly more general than BTL. Finally, we propose a new SVM-based algorithm for rank aggregation from pairwise data, and show that this converges to an optimal ranking under an even more general condition that we term 'generalized low-noise'. In all cases, we provide explicit sample complexity bounds for exact recovery of an optimal ranking. Our experiments confirm our theoretical findings and help to shed light on the statistical behavior of various rank aggregation algorithms.

Combining latent factor model with location features for event-based group recommendation

Abstract: Groups play an essential role in many social websites which promote users' interactions and accelerate the diffusion of information. Recommending groups that users are really interested to join is significant for both users and social media. While traditional group recommendation problem has been extensively studied, we focus on a new type of the problem, i.e., event-based group recommendation. Unlike the other forms of groups, users join this type of groups mainly for participating offline events organized by group members or inviting other users to attend events sponsored by them. These characteristics determine that previously proposed approaches for group recommendation cannot be adapted to the new problem easily as they ignore the geographical influence and other explicit features of groups and users. In this paper, we propose a method called Pairwise Tag enhAnced and featuRe-based Matrix factorIzation for Group recommendAtioN (PTARMIGAN), which considers location features, social features, and implicit patterns simultaneously in a unified model. More specifically, we exploit matrix factorization to model interactions between users and groups. Meanwhile, we incorporate their profile information into pairwise enhanced latent factors respectively. We also utilize the linear model to capture explicit features. Due to the reinforcement between explicit features and implicit patterns, our approach can provide better group recommendations. We conducted a comprehensive performance evaluation on real word data sets and the experimental results demonstrate the effectiveness of our method.

Integration of an Index to Preserve the Semantic Interpretability in the Multiobjective Evolutionary Rule Selection and Tuning of Linguistic Fuzzy Systems

Abstract: In this paper, we propose an index that helps preserve the semantic interpretability of linguistic fuzzy models while a tuning of the membership functions (MFs) is performed. The proposed index is the aggregation of three metrics that preserve the original meanings of the MFs as much as possible while a tuning of their definition parameters is performed. Additionally, rule-selection mechanisms can be used to reduce the model complexity, which involves another important interpretability aspect. To this end, we propose a postprocessing multiobjective evolutionary algorithm that performs rule selection and tuning of fuzzy-rule-based systems with three objectives: accuracy, semantic interpretability maximization, and complexity minimization. We tested our approach on nine real-world regression datasets. In order to analyze the interaction between the fuzzy-rule-selection approach and the tuning approach, these are also individually proved in a multiobjective framework and compared with their respective single-objective counterparts. We compared the different approaches by applying nonparametric statistical tests for pairwise and multiple comparisons, taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective-based approaches. Results confirm the effectiveness of our approach, and a wide range of solutions is obtained, which are not only more interpretable but are also more accurate.

Jointly Combining Implicit Constraints Improves Temporal Ordering

Abstract: Previous work on ordering events in text has typically focused on local pairwise decisions, ignoring globally inconsistent labels. However, temporal ordering is the type of domain in which global constraints should be relatively easy to represent and reason over. This paper presents a framework that informs local decisions with two types of implicit global constraints: transitivity (A before B and B before C implies A before C) and time expression normalization (e.g. last month is before yesterday). We show how these constraints can be used to create a more densely-connected network of events, and how global consistency can be enforced by incorporating these constraints into an integer linear programming framework. We present results on two event ordering tasks, showing a 3.6% absolute increase in the accuracy of before/after classification over a pairwise model.